Elliptic Loci of SU(3) VacuaDownload PDF

17 May 2023OpenReview Archive Direct UploadReaders: Everyone
Abstract: The space of vacua of many four-dimensional, N=2 supersymmetric gauge theories can famously be identified with a family of complex curves. For gauge group SU(2), this gives a fully explicit description of the low-energy effective theory in terms of an elliptic curve and associated modular fundamental domain. The two-dimensional space of vacua for gauge group SU(3) parametrizes an intricate family of genus two curves. We analyze this family using the so-called Rosenhain form for these curves. We demonstrate that two natural one-dimensional subloci of the space of SU(3) vacua, Eu and Ev, each parametrize a family of elliptic curves. For these elliptic loci, we describe the order parameters and fundamental domains explicitly. The locus Eu contains the points where mutually local dyons become massless, and is a fundamental domain for a classical congruence subgroup. Moreover, the locus Ev contains the superconformal Argyres-Douglas points, and is a fundamental domain for a Fricke group.
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